New England Patriots tight end Rob Gronkowski catches a touchdown pass against the Denver Broncos in the AFC Divisional playoff game in Foxborough, Massachusetts. Photograph: Jessica Rinaldi/Reuters

The New England Patriots look increasingly likely to have their record-breaking tight end Rob Gronkowski available for Sunday's Super Bowl against the New York Giants, with the team's head coach Bill Belichick confirming that the player was progressing well in his recovery from a high ankle sprain.

Gronkowski, who caught 17 touchdown passes this season – the most ever by a tight end – participated in Patriots training on Thursday for the first time since suffering a high ankle sprain during a 23-20 win over the Baltimore Ravens in the AFC Championship game. Afterwards Belichick had said that the key would be how Gronkowski's ankle responded after a night's rest and on Friday he confirmed that the signs were positive.

"I think he was OK this morning," said Belichick at his final press conference before Super Bowl XLVI. "I don't think we had any setbacks and we'll see how he goes out there today, but Rob's worked extremely hard, he's had treatment morning noon and night and he's got better on a daily basis.

"Hopefully he'll be able to continue that progress today, tomorrow and all day Sunday and see where that takes us, but I think that he's coming along. We'll see where he gets to but certainly moving in the right direction, he's getting better on a daily basis."

During Super Bowl week only one journalist is permitted to attend each team's practice sessions, filing a short pool report each day for the rest of the media covering the event to share. As such details of Gronkowski's training yesterday are thin on the ground, prompting one reporter to ask on Friday if Belichick could expand on what sort of activities Gronkowski had performed in training.

"He practiced on a limited basis and did some of the things that we did in practice but not all of them," responded Belichick with a grin. "Is that the answer to that question you were looking for?"

Belichick was similarly vague when one reporter raised the issue of his own long-term future. Reminded that he will be turning 60 this April, the coach was asked if a victory on Sunday might lead him to consider this as the ideal moment to "ride off into the sunset".

"Right now I'm really thinking about what's the best thing I could do to help our football team on Sunday against the Giants," said Belichick. "I want to really try to do a good job, in the job that I have.

"I've enjoyed … I enjoy all the aspects of the job, I enjoy the team-building, the drafting, the free agents, the team acquisitions, those kind of things. I enjoy bringing in the young players and working with the guys who haven't been in the NFL and teaching them the basic fundamentals and how to become a professional football player for the New England Patriots. And I enjoy working with the veteran players, the Tom Bradys, the Vince Wilforks and the Wes Welkers who can do really special things because of not only their talent but experience.

"And I enjoy the competition on a weekly basis. Not just on Sundays but the preparation leading up into the game. I enjoy all of it. It beat sworking. It's fun to address those challenges on a daily basis. So right now I'm really focussed on the game and that's where my energies are going to go is toward doing the best I can for the New England Patriots and that's the Giants on Sunday."